Multiquadric B-splines

AbstractOur purpose in this paper is to show that the analogy between polynomial splines and generalized multiquadrics is very strong. In particular, combinations of multiquadrics, calledψ-splines are defined that are analogues of polynomial B-splines. This paper includes global linear independence, polynomial reproduction, and quasi-interpolation results for the span of theψ-splines on non-uniform bi-infinite meshes which parallel those for polynomial B-splines. There are also results concerning the relationship between certain semi-infinite and bi-infinite combinations ofψ-splines. These results enable us to obtain error estimates for quasi-interpolation schemes involving multiquadrics based on a finite number of centres